The British are a conservative lot at heart. I don't say that gladly. It is, for those on the left, a miserable fact – but one that Labour's current leadership seems to be recognising, just as Tony Blair did. And before you wonder what this has got to do with art – well, it has everything to do with art.

For years, the fame of Britain's young (now middle-aged) conceptual artists has been treated as a matter of national pride. To judge from the apparent public interest in the Turner prize or Frieze art fair, you'd think everyone believes in the genius of the avant garde. But we're much shallower than that: for all our desire to seem au fait, Britain only gives its full and authoritative acclaim to the safe and proven.

I find it quite tasteless (and I'm sure he does, too) that David Hockney is widely described as Britain's "greatest living artist" now Lucian Freud is gone. Hockney has inherited the job, it seems. What is the basis for this assumption? It comes down to two things, apparently: one, Hockney is no longer young; and two, he's a craftsman who makes his paintings with his own two hands. These are the most conservative grounds conceivable.

What is fascinating is that none of the pundits chucking this "greatness" stuff about would consider describing, say, Rachel Whiteread or Antony Gormley as such. Despite their celebrity, they do not qualify. Nor, it seems, does Bridget Riley. Too abstract! And the wrong gender.

I have long suspected that a lot of the fuss made over contemporary art in Britain is totally insincere. In the end, the British middle class is in the same place it was in 1993, when Whiteread won the Turner prize: amused and intrigued by "modern art", enjoying the debates it provokes, – but, deep down, completely sceptical of any grand claims for its quality.

The sophisticated alternative view here might be to say that greatness is a myth, and that everyone should be less hyperbolic. But I am not sophisticated, and I think honesty matters. I don't think I'm especially guilty of hyping the latest art, but I do see value in my generation, and I do believe something real and new entered British culture in the 1990s. British conservatism when it comes to this period is truly misplaced.

To really see the foolishness of this attitude, we might take a second look at Lucian Freud. He did not earn his extraordinary reputation by being a safe pair of hands. He was not just a decent craftsman who worked patiently until he became great. He was a profoundly original, scathing, cruel, sensual, serious observer of the human condition. His art attained a profundity that was paralleled in modern British culture by, say, the plays of Harold Pinter, and the poetry of TS Eliot.

In other words, Freud was a modern artist of a deeply unsettling kind, and no "conservative". The truth is, his job of "greatest living British artist" should continue to stand vacant for a while, out of respect for one of the truly creative lives of the last 100 years. And when the time comes to fill it, let's not be so sure the new occupant will be old, a Proper Painter, and male. These assumptions betray a parochial and timid attitude beneath our oh-so-groovy culture. Most of all, they show little grasp of what greatness is, how rare it is, how special.